##############ECHO OF PROBLEM################# ##############temp/mtest1postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(10.0); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y1 (double x) { return(c(1.0) + cos(c(x))); } double exact_soln_y2 (double x) { return(c(1.0) + sin(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y1[1] (closed_form) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 y2[1] (closed_form) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1993346653975308 y1[1] (closed_form) = 1.980198542488623 y1[1] (numeric) = 1.980198542488624 absolute error = 2.220446049250313e-16 relative error = 1.121324958890111e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 y2[1] (closed_form) = 1.198017214663721 y2[1] (numeric) = 1.198017214663721 absolute error = 2.220446049250313e-16 relative error = 1.853434176130419e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1941 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1941 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3086027973348146 y1[1] (closed_form) = 1.952758868926032 y1[1] (numeric) = 1.952758868926032 absolute error = 2.220446049250313e-16 relative error = 1.137081533508283e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 y2[1] (closed_form) = 1.303727736110465 y2[1] (numeric) = 1.303727736110465 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2894 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2894 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4079374627323454 y1[1] (closed_form) = 1.917941018085094 y1[1] (numeric) = 1.917941018085095 absolute error = 2.220446049250313e-16 relative error = 1.157723844640043e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 y2[1] (closed_form) = 1.396716885595887 y2[1] (numeric) = 1.396716885595888 absolute error = 2.220446049250313e-16 relative error = 1.589761011805191e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3642 Order of pole (three term test) = 32.16 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3642 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5072721281298761 y1[1] (closed_form) = 1.874072943805317 y1[1] (numeric) = 1.874072943805317 absolute error = 4.440892098500626e-16 relative error = 2.369647410566297e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 y2[1] (closed_form) = 1.485794698311445 y2[1] (numeric) = 1.485794698311445 absolute error = 2.220446049250313e-16 relative error = 1.49445010927403e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4246 Order of pole (three term test) = 32.24 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4246 Order of pole (three term test) = 32.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6066067935274063 y1[1] (closed_form) = 1.821587153041113 y1[1] (numeric) = 1.821587153041113 absolute error = 2.220446049250313e-16 relative error = 1.218962290957812e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 y2[1] (closed_form) = 1.570082932526311 y2[1] (numeric) = 1.570082932526311 absolute error = 4.440892098500626e-16 relative error = 2.828444285649992e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4684 Order of pole (three term test) = 32.32 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4684 Order of pole (three term test) = 32.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7059414589249365 y1[1] (closed_form) = 1.761001117094475 y1[1] (numeric) = 1.761001117094475 absolute error = 2.220446049250313e-16 relative error = 1.260899852757554e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 y2[1] (closed_form) = 1.648750568231705 y2[1] (numeric) = 1.648750568231706 absolute error = 1.110223024625157e-15 relative error = 6.733723378278362e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4937 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4937 Order of pole (three term test) = 32.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8052761243224668 y1[1] (closed_form) = 1.692912169728453 y1[1] (numeric) = 1.692912169728453 absolute error = 8.881784197001252e-16 relative error = 5.246453038627461e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 y2[1] (closed_form) = 1.721022000387094 y2[1] (numeric) = 1.721022000387096 absolute error = 1.332267629550188e-15 relative error = 7.741142351756879e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4996 Order of pole (three term test) = 32.52 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4996 Order of pole (three term test) = 32.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.904610789719997 y1[1] (closed_form) = 1.617991617895495 y1[1] (numeric) = 1.617991617895495 absolute error = 8.881784197001252e-16 relative error = 5.489388263057688e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 y2[1] (closed_form) = 1.786184685815558 y2[1] (numeric) = 1.786184685815559 absolute error = 1.110223024625157e-15 relative error = 6.215611596279235e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4859 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4859 Order of pole (three term test) = 32.38 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.003945455117527 y1[1] (closed_form) = 1.536978123144536 y1[1] (numeric) = 1.536978123144534 absolute error = 1.554312234475219e-15 relative error = 1.011278046882814e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753071 y2[1] (closed_form) = 1.843596168355554 y2[1] (numeric) = 1.843596168355555 absolute error = 1.110223024625157e-15 relative error = 6.022051052619894e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.453 Order of pole (three term test) = 32.71 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.453 Order of pole (three term test) = 32.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.103280120515058 y1[1] (closed_form) = 1.450670418961292 y1[1] (numeric) = 1.45067041896129 absolute error = 2.220446049250313e-15 relative error = 1.530634402016824e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753071 y2[1] (closed_form) = 1.892690413006241 y2[1] (numeric) = 1.892690413006243 absolute error = 1.554312234475219e-15 relative error = 8.212184220907204e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4023 Order of pole (three term test) = 32.8 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4023 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.202614785912588 y1[1] (closed_form) = 1.359919435843434 y1[1] (numeric) = 1.359919435843431 absolute error = 3.108624468950438e-15 relative error = 2.285888698268689e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753071 y2[1] (closed_form) = 1.932983386616366 y2[1] (numeric) = 1.932983386616368 absolute error = 1.77635683940025e-15 relative error = 9.189716019803532e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3358 Order of pole (three term test) = 32.87 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3358 Order of pole (three term test) = 32.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.301949451310118 y1[1] (closed_form) = 1.265619911751605 y1[1] (numeric) = 1.265619911751601 absolute error = 3.774758283725532e-15 relative error = 2.982537054510548e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753071 y2[1] (closed_form) = 1.9640778300952 y2[1] (numeric) = 1.964077830095202 absolute error = 1.554312234475219e-15 relative error = 7.913699806895537e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2561 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2561 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.401284116707648 y1[1] (closed_form) = 1.168701570651062 y1[1] (numeric) = 1.168701570651058 absolute error = 4.662936703425657e-15 relative error = 3.989843789486842e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753071 y2[1] (closed_form) = 1.985667175095054 y2[1] (numeric) = 1.985667175095056 absolute error = 1.554312234475219e-15 relative error = 7.827657393796691e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1663 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1663 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.505055086899324 y1[1] (closed_form) = 1.065693895500464 y1[1] (numeric) = 1.065693895500458 absolute error = 5.329070518200751e-15 relative error = 5.000563989998413e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.007275776712777138 y2[1] (closed_form) = 1.997839822864358 y2[1] (numeric) = 1.997839822864359 absolute error = 8.881784197001252e-16 relative error = 4.445693841594964e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.007275776712777138 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06555 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06555 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.599998651048259 y1[1] (closed_form) = 0.97080182607529 y1[1] (numeric) = 0.9708018260752947 absolute error = 4.773959005888173e-15 relative error = 4.917542260080104e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001474401342213636 y2[1] (closed_form) = 1.999573642429342 y2[1] (numeric) = 1.999573642429342 absolute error = 2.220446049250313e-16 relative error = 1.11045975108605e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001474401342213636 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! Maximum Iterations Reached before Solution Completed! diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 16.07 %